Extremal argument — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Extremal argument — a problem-solving techniques concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 8
1988 AMC 8 Problem 16 • 1991 AMC 8 Problem 6 • 1991 AMC 8 Problem 14 • 1991 AMC 8 Problem 19 • 1992 AMC 8 Problem 19 • 2012 AMC 8 Problem 17 • 2019 AMC 8 Problem 19 • 2024 AMC 8 Problem 7 • 2024 AMC 8 Problem 16 • 2025 AMC 8 Problem 15 • 2026 AMC 8 Problem 22
AMC 10
2002 AMC 10A Problem 21 • 2005 AMC 10B Problem 25 • 2008 AMC 10B Problem 4 • 2012 AMC 10B Problem 15 • 2016 AMC 10B Problem 6 • 2018 AMC 10A Problem 17 • 2019 AMC 10A Problem 4 • 2019 AMC 10A Problem 5 • 2022 AMC 10B Problem 14 • 2022 AMC 10B Problem 24 • 2023 AMC 10B Problem 10 • 2024 AMC 10A Problem 20 • 2024 AMC 10B Problem 12 • 2025 AMC 10A Problem 21
AMC 12
1957 AMC 12 Problem 17 • 1961 AMC 12 Problem 39 • 1964 AMC 12 Problem 39 • 1968 AMC 12 Problem 30 • 1978 AMC 12 Problem 10 • 1978 AMC 12 Problem 16 • 1982 AMC 12 Problem 29 • 1984 AMC 12 Problem 3 • 1985 AMC 12 Problem 14 • 1989 AMC 12 Problem 11 • 1989 AMC 12 Problem 25 • 2002 AMC 12A Problem 15 • 2008 AMC 12B Problem 3 • 2010 AMC 12B Problem 6 • 2010 AMC 12B Problem 14 • 2012 AMC 12A Problem 17 • 2013 AMC 12B Problem 17 • 2015 AMC 12B Problem 5 • 2018 AMC 12A Problem 12 • 2021 AMC 12A Fall Problem 16 • 2021 AMC 12B Fall Problem 14 • 2023 AMC 12B Problem 5 • 2025 AMC 12A Problem 13 • 2025 AMC 12A Problem 15
AIME
1984 AIME Problem 14 • 1985 AIME Problem 8 • 1986 AIME Problem 12 • 1988 AIME Problem 4 • 1989 AIME Problem 13 • 1995 AIME Problem 10 • 2001 AIME II Problem 5 • 2002 AIME I Problem 14 • 2003 AIME II Problem 12 • 2004 AIME I Problem 5 • 2006 AIME I Problem 2 • 2008 AIME II Problem 10 • 2009 AIME I Problem 13 • 2009 AIME II Problem 12 • 2010 AIME I Problem 12 • 2022 AIME I Problem 7 • 2024 AIME II Problem 9 • 2026 AIME I Problem 11 • 2026 AIME I Problem 15